Abstract

In most phase unwrapping algorithms, the image reconstruction results are obtained by shifting the phase jumps in the wrapped phase map by 2π. The performance of such algorithms is degraded by the presence of speckle noise, residual noise, noise at the height discontinuities and holes in the wrapped phase map. Thus, a filtering operation is performed prior to the unwrapping process in order to remove the noise. However, the filtering process smears the phase jumps in the wrapped phase map and therefore causes a phase shifting error during the reconstruction process. Moreover, the noise errors, hole errors and shifting errors are accumulated path-by-path during unwrapping. Accordingly, the present study proposes a new rotation algorithm for phase unwrapping applications which resolves the noise error, the error of hole, the shifting error. Existing phase unwrapping algorithms are designed to operate only on those pixels whose phase values have no noise or holes. Or they are designed to operate the three-dimensional unwrapping paths in the row and column directions to avoid the noise or holes. By contrast, the rotation algorithm proposed in this study operates on all the pixels in the wrapped phase map, including those affected by noise or holes. As a result, the noise errors and hole errors produced in existing 2π phase shifting unwrapping algorithms are eliminated. Furthermore, since in the proposed approach, the wrapped phase map is not filtered prior to the unwrapping process, the phase shifting errors induced in existing algorithms are also eliminated. The robustness of the proposed algorithm to various noise errors, hole errors and phase shifting errors is demonstrated both numerically and experimentally.

Figures (19)

2D wrapped phase. Note that the blue-solid lines represent wrapped phase lines. Note also that Phase 1 extends from a point to the left of D2 to D2 while Phase 2 extends fully from D3 to D4. Finally, note that the red triangles represent noise or holes.

Results of first relative rotation procedure. Note that the red line indicates the result obtained by rotating Phase 1 about C1 byθ1, while the blue line indicates the result obtained by rotating Phase 2 about C2 byθ2. Note also that the phase values, noise and holes are all preserved in the rotation results.

Results of second relative rotation procedure in which rotated Phase 1 from D1’ to D2’ is further rotated by θ''fix leading to new rotated Phase 1 from D1” to D2”. A stitching process is then performed in which new rotated Phase 1 is shifted in the y-direction and stitched to Phase 2 from D3′ to D4’.

Starting position for new first relative rotation procedure based on stitching results shown in Fig. 3. The final cycle of the relative rotation stage is terminated when eliminating all of the 2π phase jumps. Totally, two cycles of the relative rotation stage are implemented in Fig. 1.